Question

A particle with a lifetime of 2 X 10^-6 s moves through the laboratory with a speed of 0.9 c. It’s lifetime, as measured by an observer in the laboratory, is ___________

(a) 2 X 10^-6 s

(b) 3.2 X 10^-6 s

(c) 4.6 X 10^-6 s

(d) 5.4 X 10^-6 s

This question was addressed to me during an internship interview.

My doubt stems from Lorentz Transformation Equations in division Ultrasonics & Relativity of Engineering Physics I

Answer 1

Correct answer is (c) 4.6 X 10^-6 s

To explain I would say: Δt0 = 2 X 10^-6 s, v = 0.9c, Δt =?

Δt = \(\frac{\Delta t_0}{\sqrt{1-\frac{v^2}{c^2}}}\)

= 2 X 10^-6 s/0.43

= 4.6 X 10^-6s.